Trends, time-varying and nonlinear time series models for NGRIP and VOSTOK paleoclimate data

In order to gain further insights into stochastic behaviour of paleoclimate data, including timescales at and below Milankovitch forcing, three specific questions are discussed using δ ¹⁸O NGRIP and Vostok Deuterium content data. A comparison of ordinary and time-varying coefficients autoregressive (AR) models shows that both data sets are distinguishable from data generated by suitable low-order AR processes in contrast to earlier conclusions. A harmonic regression analysis clearly distinguishing between discrete and continuous spectra detects cycles corresponding to variations of eccentricity, obliquity and precession. Contribution of eccentricity to the total variance in the last 422,766-year Vostok data is close to, while the variance reduction delivered jointly by obliquity and precession is substantially smaller than a previous recent finding. A harmonic regression analysis with time-varying frequencies and amplitudes is also performed. This approach delivers a gain over the constant frequency model at any reasonable significance level. It is demonstrated that variations of frequencies are at least partly due to real variations and not merely to timescale uncertainties. In order to consider nonlinearity in paleoclimate data, threshold autoregressive (TAR) models are applied to time series examined. A bivariate TAR model describing simultaneous NGRIP and Vostok data exhibits three fix points and one limit cycle related to a part of Dansgaard–Oeschger events. The model selected suggests that Greenland has a primary role in the Greenland–Antarctica climate variation relationship.     

Power and cross-power spectral studies of electric parameters under fair weather conditions in the atmospheric surface layer

Power spectral and cross-spectral studies of atmospheric electrical parameters for different months of the year are presented. The data represent fair weather conditions and the frequency range is from 0.01 to 0.3 cph. The analysis shows spectral peaks in the atmospheric electric parameters for frequencies corresponding to the diurnal wave; in many cases large variances are noted for the frequencies 0.083, 0.125 and 0.17 cph. Annual cycles in the spectra are also observed. In general, fairly small variances are obtained for frequencies above 0.05 cph. High coherences for the atmospheric electric parameters are observed in the lower frequency part of the spectra and in some cases in other parts as well (i.e., 0.083, 0.125 and 0.17 cph). Phase relationships of the electric components are also presented.     

Spectra of surface wind speed and air temperature over the ocean in the mesoscale frequency range in JASIN-1978

Based on the data from an array of buoys during the JASIN-1978 field experiment made in an area northwest of Scotland, power spectra of surface wind speed and air temperature over the ocean in the mesoscale frequency range were studied. The averaged composite spectrum of wind speed for the whole period shows the existence of a spectral gap in the frequency range from 10^–4 to 5 × 10^–3 Hz. However, significant peaks in this range are often seen in particular spectra under certain weather conditions. Mesoscale spectral peaks of wind speed occur in 14 segments of the data record, approximately 10% of the total duration of the observations. In 4 of these segments, the mesoscale spectral peaks of both wind speed and air temperature occurred simultaneously. Several wave patterns of mesoscale atmospheric disturbances when mesoscale spectral peaks were seen are derived from phase differences between buoys. Significant mesoscale peaks in spectra appear in relatively strong winds and unstable or near-neutral atmospheric conditions, and none in stable atmospheric conditions. A criterion of wind speed and atmospheric stability is found for the mesoscale spectral peak appearance.     

Taylor's hypothesis and spectra of velocity and temperature derivatives in a turbulent shear flow

Spectral densities of temporal velocity and temperature derivatives, measured in the atmospheric turbulent boundary layer and on the axis of a turbulent plane jet, are compared with the spectral densities of the ratios of these derivatives and of the local longitudinal instantaneous velocity. The comparison between the spectral densities, when both are normalized such that the areas under the spectra are equal, shows that the corrected spectrum is lower than the measured spectrum at frequencies larger than about one-seventh of the Kolmogorov frequency while the opposite trend is observed at low frequencies. A qualitatively similar result has been obtained when the measured velocity derivative spectrum is compared with that corrected using Lumley's method. While the unnormalized spectral densities and moments of the derivatives, as corrected by Lumley's method are smaller than the corresponding measured quantities, the opposite trend is found when the correction is made by dividing the temporal derivative by the longitudinal instantaneous velocity.     

Decadal time scale variability recorded in the Quelccaya summit ice core δ18O isotopic ratio series and its relation with the sea surface temperature

 The spectral characteristics of the δ¹⁸O isotopic ratio time series of the Quelccaya ice cap summit core are investigated with the multi taper method (MTM), the singular spectrum analysis (SSA) and the wavelet transform (WT) techniques for the 500 y long 1485–1984 period. The most significant (at the 99.8% level) cycle according to the MTM F-test has a period centered at 14.4 y while the largest variance explaining oscillation according to the SSA technique has a period centered at 12.9 y. The stability over time of these periods is investigated by performing evolutive MTM and SSA on the 500 y long δ¹⁸O series with a 100 y wide moving window. It is shown that the cycles with largest amplitude and that the oscillations with largest extracting variance have corresponding periods aggregated around 13.5 y that are very stable over the period between 1485 and 1984. The WT of the same isotopic time series reveals the existence of a main oscillation around 12 y which are also very stable in time. The relation between the isotopic data at Quelccaya and the annual sea surface temperature (SST) field anomalies is then evaluated for the overlapping 1919–1984 period. Significant global correlation and significant coherency at 12.1 y are found between the isotopic series and the annual global sea surface temperature (GSST) series. Moreover, the correlation between the low (over 8 y) frequency component of the isotopic time series and the annual SST field point out significant values in the tropical North Atlantic. This region is characterized by a main SST variability at 12.8 y. The Quelccaya δ¹⁸O isotopic ratio series may therefore be considered as a good recorder of the tropical North Atlantic SSTs. This may be explained by the following mechanism: the water vapor amount evaporated by the tropical North Atlantic is function of the SST. So is the water vapor δ¹⁸O isotopic ratio. This water vapor is advected during the rainy season by northeast winds and precipitates at the Quelccaya summit with its tropical North Atlantic isotopic signature. It is also suggested from this described stability of the decadal time scale variability observed in the Quelccaya isotopic series, that the decadal time scale GSST variability was also stable during the last five centuries. Received: 12 February 1997 / Accepted: 9 September 1997     

Local similarity of spectral and cospectral characteristics in the stable-continuous boundary layer

The local similarity theory, presented in the recent papers of Sorbjan (1986a, b), is extended by taking into consideration spectral (u, v, w, ) and cospectral (uw, w, u) densities in the stable-continuous boundary layer. The resulting universal expressions for spectra, cospectra and the reduced frequencies of their peaks are in agreement with empirical data from the Kansas 1968 surface-layer and Minnesota 1973 boundary-layer experiments. In addition, the universal functions for the structure parameters and the dissipation rates are also derived and shown to fit the empirical data well.On leave from Institute of Environmental Engineering, Warsaw Polytechnic University, 00653 Warsaw, Poland.     

Multifractal detrended fluctuation analysis of the δ 18 O record of NGRIP ice core

The multifractal properties and scaling behaviors of the long-term and recent 2000-year δ ¹⁸ O records of NGRIP ice core are investigated by the multifractal detrended fluctuation analysis method. The generalized Hurst exponents, multifractal scaling exponents, and singularity spectrums of two δ ¹⁸ O records are derived to verify the multifractiality of two records. And the multifractal behaviors of two records are obviously different, which may reflect the climate change of the recent 2000-year time is quite different from one of the long-term time. In addition, the probability distribution analysis of two δ ¹⁸ O records is presented to manifest the different multifractality between two δ ¹⁸ O records of NGRIP ice core. Our results will be helpful to research the climate change.     

Seasonal variations of spectra of wind speed and air temperature in the mesoscale frequency range

Seasonal variations of the spectra of wind speed and air temperature in the mesoscale frequency range from 1.3 × 10^-4 to 1.5 × 10^-3 Hz (10 min to 2 h periods) have been studied through observations over land for one year. Spectrographs [time series of isopleths of spectral densities, f · S(f) vs f] of wind speed and air temperature contain occasional peaks that are attributed to short-lived mesoscale atmospheric activity with narrow frequency bands. Significant spectral peaks of wind speed were found in 19% of the total observations in winter, and in 15–16% in the other seasons; for air temperature, they occured in 12% of observations in autumn, and in 16–19% in the other seasons. The peaks most often occurred in the period range from 30 min to 1 h; most had durations less than 24 h. Mesoscale fluctuations of wind speed and air temperature were highly correlated, and in most cases, phase differences were 90–180 ° with air temperature leading wind speed. Significant spectral peaks of wind speed often occurred during northerly seasonal cold winds in winter, and accompanied tropical and/or mid-latitude cyclones in the other seasons. When the peaks occurred, wind speed was usually relatively high and the atmospheric surface layer was unstable.     

Characterizing atmospheric circulation signals in Greenland ice cores: insights from a weather regime approach

Greenland ice cores offer seasonal to annual records of δ¹⁸O, a proxy for precipitation-weighted temperature, over the last few centuries to millennia. Here, we investigate the regional footprints of the North Atlantic weather regimes on Greenland isotope and climate variability, using a compilation of 22 different shallow ice-cores and the atmospheric pressure conditions from the twentieth century reanalysis (20CR). As a first step we have verified that the leading modes of winter and annual δ¹⁸O are well correlated with oceanic (Atlantic multidecadal oscillation) and atmospheric [North Atlantic oscillation (NAO)] indices respectively, and also marginally with external forcings, thus confirming earlier studies. The link between weather regimes and Greenland precipitation, precipitation-weighted temperature and δ¹⁸O is further explored by using an isotope simulation from the LMDZ-iso model, where the 3-dimensional wind fields are nudged to those of 20CR. In winter, the NAO+ and NAO? regimes in LMDZ-iso produce the largest isotopic changes over the entire Greenland region, with maximum anomalies in the South. Likewise, the Scandinavian blocking and the Atlantic ridge also show remarkable imprints on isotopic composition over the region. To assess the robustness and model dependency of our findings, a second isotope simulation from the isotopic model is also explored. The percentage of Greenland δ¹⁸O variance explained by the ensemble of weather regimes is increased by a factor near two in both LMDZ-iso and IsoGSM when compared to the contribution of the NAO index only. Similarly, weather regimes provide a net gain in the δ¹⁸O variance explained of similar magnitude for the whole set of ice core records. Greenland δ¹⁸O also appears to be locally affected by the low-frequency variations in the centres of action of the weather regimes, with clearer imprints in the LMDZ-iso simulation. This study opens the possibility for reconstructing past changes in the frequencies of occurrence of the weather regimes, which would rely on the sensitive regions identified here, and the use of additional proxies over the North Atlantic region.     

Spring-summer temperatures since AD 1780 reconstructed from stable oxygen isotope ratios in white spruce tree-rings from the Mackenzie Delta,northwestern Canada

High-latitude δ¹⁸O archives deriving from meteoric water (e.g., tree-rings and ice-cores) can provide valuable information on past temperature variability, but stationarity of temperature signals in these archives depends on the stability of moisture source/trajectory and precipitation seasonality, both of which can be affected by atmospheric circulation changes. A tree-ring δ¹⁸O record (AD 1780–2003) from the Mackenzie Delta is evaluated as a temperature proxy based on linear regression diagnostics. The primary source of moisture for this region is the North Pacific and, thus, North Pacific atmospheric circulation variability could potentially affect the tree-ring δ¹⁸O-temperature signal. Over the instrumental period (AD 1892–2003), tree-ring δ¹⁸O explained 29 % of interannual variability in April–July minimum temperatures, and the explained variability increases substantially at lower-frequencies. A split-period calibration/verification analysis found the δ¹⁸O-temperature relation was time-stable, which supported a temperature reconstruction back to AD 1780. The stability of the δ¹⁸O-temperature signal indirectly implies the study region is insensitive to North Pacific circulation effects, since North Pacific circulation was not constant over the calibration period. Simulations from the NASA-GISS ModelE isotope-enabled general circulation model confirm that meteoric δ¹⁸O and precipitation seasonality in the study region are likely insensitive to North Pacific circulation effects, highlighting the paleoclimatic value of tree-ring and possibly other δ¹⁸O records from this region. Our δ¹⁸O-based temperature reconstruction is the first of its kind in northwestern North America, and one of few worldwide, and provides a long-term context for evaluating recent climate warming in the Mackenzie Delta region.     

华北地区夏季降水日变化的时空分布特征

利用2008~2014年间全国自动站观测降水和CMORPH[CPC（Climate Prediction Center）morphing technique]卫星反演降水资料融合而成的0.1°×0.1°小时降水产品揭示了华北夏季降水的日变化特征,发现华北多数地区夏季降水量和降水频率日变化呈现出明显的双峰特征且存在明显的区域性差异。在太行山以西地区,降水量和降水频率的日峰值出现在傍晚18:00左右（北京时）,规律性最强;而在太行山以东的平原和沿海地区,日峰值一般出现在上午。研究不同持续时间降水对总降水的贡献发现短时降水对傍晚的降水日峰值贡献较大,而长时降水则对凌晨的峰值影响更大。分析不同强度降水对总降水量的贡献结果表明,0.1~10 mm h-1强度降水较其它强度降水对夏季华北地区总降水量贡献更大,随着降水强度的增加降水量日变化的峰值个数增加。     

A climate-isotope regression model with seasonally-varying and time-integrated relationships

This study investigates multivariable and multiscalar climate-??¹⁸O relationships, through the use of statistical modeling and simulation. Three simulations, of increasing complexity, are used to generate time series of daily precipitation ??¹⁸O. The first simulation uses a simple local predictor (daily rainfall amount). The second simulation uses the same local predictor plus a larger-scale climate variable (a daily NAO index), and the third simulation uses the same local and non-local predictors, but with varying seasonal effect. Since these simulations all operate at the daily timescale, they can be used to investigate the climate-??¹⁸O patterns that arise at daily-interannual timescales. These simulations show that (1) complex links exist between climate-??¹⁸O relationships at different timescales, (2) the short-timescale relationships that underlie monthly predictor-??¹⁸O relationships can be recovered using only monthly ??¹⁸O and daily predictor variables, (3) a comparison between the simulations and observational data can elucidate the physical processes at work. The regression models developed are then applied to a 2-year dataset of monthly precipitation ??¹⁸O from Dublin and compared with event-scale data from the same site, which illustrates that the methodology works, and that the third regression model explains about 55% of the variance in ??¹⁸O at this site. The methodology introduced here can potentially be applied to historic monthly ??¹⁸O data, to better understand how multiple-integrated influences at short timescales give rise to climate-??¹⁸O patterns at monthly-interannual timescales.     

Some aspects of the interpretation of spectra in meteorology

The meaningfulness of spectral presentations, and of spectral peaks in particular, is considered by the use of simple examples. First, we derive analytically the spectra of sinusoidal finite-length waves and subject the spectra to several area-conserving transformations. The peak of the logarithmic spectrum (power density per unit natural logarithm of frequency) is shown to be the most appropriate for defining the scales (or frequencies) of the waves. The advantage of the logarithmic spectrum becomes even more apparent when a wave consisting of the positive part of a sine wave is considered. In that case, the conventional frequency presentation is misleading because in addition to the erroneous location of the spectral peak, an increase of power density towards low frequencies occurs, giving the spectra the appearance of red noise. For the same wave, it is shown that the logarithmic spectrum has a single peak at the position corresponding with the actual wave frequency.     

A simple spectral model for the modification of turbulence in flow over gentle hills

A model is presented which calculates the changes of the velocity variances and stress uw in flow over gentle isolated hills. At intermediate frequencies spectra of the velocity components are modified according to rapid distortion theory. At low frequencies spectral densities change in proportion to the square of the mean wind. The inner and outer layer of the flow are distinguished. Streamline curvature effects are accounted for in the vertical velocity variance and the covariance.The sensitivity of the model to several parameters is investigated. Then, its results are compared with measurements of turbulent flow over various hills and an escarpment. The model is able to simulate the structure of the modified variance and covariance fields although larger differences occur at individual positions. The calculated modified spectra compare well with observed spectra.     

Modelling velocity spectra in the lower part of the planetary boundary layer

Principles used when constructing models for velocity spectra are reviewed. Based upon data from the Kansas and Minnesota experiments, simple spectral models are set up for all velocity components in stable air at low heights, and for the vertical spectrum in unstable air through a larger part of the planetary boundary layer. Knowledge of the variation with stability of the (reduced) frequency % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaccaGae8NKby% kaaa!37B5!\[f\] _m for the spectral maximum is utilized in this modelling. Stable spectra may be normalized so that they adhere to one curve only, irrespective of stability, and unstable w-spectra may also be normalized to fit one curve.The problem of using filtered velocity variances when modelling spectra is discussed. A simplified procedure to provide a first estimate of the filter effect is given.In stable, horizontal velocity spectra, there is often a gap at low frequencies. Using dimensional considerations and the spectral model previously derived, an expression for the gap frequency is found.     

Oxygen isotopic composition of Central Sierra Nevada precipitation, I. Identification of ice-phase water capture regions in winter storms

Measurements of the stable isotopic ratios of oxygen and simultaneously observed ice crystal structure in freshly fallen snow, have been used to estimate the weighted mean altitudes of ice-phase precipitation formation in winter clouds over the Central Sierra Nevada.Observations of dominant, diffusionally grown ice-crystal habits were used to estimate relatively narrow ranges of temperatures of initial formation of the precipitation particles using the Nakaya (1954) ice-crystal classification techniques. The mean oxygen isotope ratio ¹⁸O/¹⁶O for each snow sample, together with local upper air soundings, were used to estimate ranges of temperature-altitude within the clouds where the precipitating particles had captured their ice-phase water. For this initial study, snow samples were collected each five (5) to ten (10) minutes during three snowfall periods on 27 January, 26 February and 28 February, 1983.For the 27 January case, the ice formation mechanism was predominantly vapor deposition and hence the narrow range of temperatures determined by the ice-crystal habits was directly relatable to the mean δ¹⁸O value.The 26 and 28 February cases were more complicated because the solid-phase precipitation was formed by vapor deposition and by freezing of drops and droplets (which occurs without isotopic fractionation). In these cases, the oxygen isotopic composition of the snow reaching the ground was representative of solid phase precipitation which had formed at warmer temperatures than those corresponding to the primary ice-crystal habits alone. There was no apparent relationship between δ¹⁸O values and surface temperature at the sampling site.If relationships between ¹⁸O/¹⁶O and temperature-altitude are established for this geograpic region for winter snowfall conditions, this crystal habit—isotopic composition technique can provide knowledge about the regions of the clouds in which the ice-phase precipitation is forming over the Central Sierra Nevada.     

An analysis of the time scales of variability in centuries-long enso-sensitive records in the last 1000 years

We document the characteristic time scales of variability for seven climate indices whose time-dependent behavior is sensitive to some aspect of the El Niño/Southern Oscillation (ENSO). The ENSO sensitivity arises from the location of these long-term records on the periphery of the Indian and Pacific Oceans. Three of the indices are derived principally from historical sources, three others consist of tree-ring reconstructions (one of summer temperature, and the other two of winter rainfall), and one is an annual record of oxygen isotopic composition for a high-elevation glacier in Peru. Five of the seven indices sample at least portions of the Medieval Warm Period (~ A.D. 950 to 1250).Time series spectral analysis was used to identify the major time scales of variability among the different indices. We focus on two principal time scales: a high frequency band (~ 2–10 yr), which comprises most of the variability found in the modern record of ENSO activity, and a low frequency band to highlight variations on decadal to century time scales (11 <P < 150 yr). This last spectral band contains variability on time scales that are of general interest with respect to possible changes in large-scale air-sea exchanges. A technique called evolutive spectral analysis (ESA) is used to ascertain how stable each spectral peak is in time. Coherence and phase spectra are also calculated among the different indices over each full common period, and following a 91-yr window through time to examine whether the relationships change.In general, spectral power on time scales of ~ 2–6 yr is statistically significant and persists throughout most of the time intervals sampled by the different indices. Assuming that the ENSO phenomenon is the source of much of the variability at these time scales, this indicates that ENSO has been an important part of interannual climatic variations over broad areas of the circum-Pacific region throughout the last millennium. Significant coherence values were found for El Niño and reconstructed Sierra Nevada winter precipitation at ~ 2–4 yr throughout much of their common record (late 1500s to present) and between 6 and 7 yr from the mid-18th to the early 20th century.At decadal time scales each record generally tends to exhibit significant spectral power over different periods at different times. Both the Quelccaya Ice Cap ¹⁸O series and the Quinn El Niño event record exhibit significant spectral power over frequencies ~ 35 to 45 yr; however, there is low coherence between these two series at those frequencies over their common record. The Sierra Nevada winter rainfall reconstruction exhibits consistently strong variability at periods of ~ 30–60 yr.     

Turbulence Structure In Unstable Conditions Over Various Surfaces

A comprehensive study of the turbulent structure of the atmospheric boundary layer in unstable conditions has been carried out using turbulence data obtained from the Gobi desert, grassland, suburban and urban sites based on the same instrumentation, data acquisition and data processing systems. The normalized standard deviations of u and v over the suburban and urban sites are systematically smaller than those over the Gobi desert and grassland sites. However, the normalized standard deviations of w, temperature and humidity q over the suburban and urban sites are quite close to those over the Gobi desert and grassland sites. The normalized humidity standard deviations are quite similar to those of temperature over the grassland and suburban sites. The temperature and humidity spectra are found to be independentof atmospheric stability in all frequency ranges, but spectra obtained from the Gobi desert and grassland sites reveal flatter peaks than those of the suburban and urban sites in the lower frequency range. The normalized spectral curves of temperature and humidity are independent of atmospheric stability both at high and low frequencies. The spectral characteristics of humidity over the grassland and suburban sites aresimilar to those of temperature, but the humidity spectra over the Gobi desert site are quite different from temperature spectra due to evaporation and/or large eddies in the boundary layer.     

Paleoclimatic variability at frequencies ranging from 1 cycle per 10 000 years to 1 cycle per 1000 years: Evidence for nonlinear behaviour of the climate system

The paleoclimatic variability at frequencies ranging from 10^–4 cycle per year (cpy) to 10^–3 cpy is investigated using a set of three deep-sea cores from the Indian Ocean. Three frequency bands of high paleoclimatic variability are first defined using upper and lower limits of the significant spectral power concentrations: the bands are centered around the spectral maxima located at 10.3, 4.7, and 2.5 kyr. The localisation of spectral lines is then refined by high-resolution spectral analysis.Some of the resulting lines have frequencies which are close to those previously detected in other paleoclimatic records, including the precessional peak at 19 kyr. Additional lines are also in good correspondence with the response of a nonlinear climatic oscillator forced by insolation variations, including peaks at 13 kyr, 10.4 kyr and 9.4 kyr. This correspondence suggests orbital forcing. Moreover for the Indian Ocean which is influenced by the monsoon circulation, it is plausible that the precessional contribution of the forcing interact strongly with the precipitation-temperature feedback used in the model, thus emphasizing the nonlinearity of the response.     

Relationship between stable isotope ratios and drop size distribution in tropical rainfall

We carried out simultaneous measurements of drop size distribution (DSD) and stable oxygen and hydrogen isotopic compositions (??¹⁸O and ??D) of rain at the National Atmospheric Research Laboratory (NARL), Gadanki (13.5°N, 79.2°E), southern India, during September?COctober 2006, with the aim of understanding microphysical processes leading to rain formation. The MST radar at NARL was operated continuously during rain events, while rain samples were collected at very short time intervals (<1?h), to capture small changes (>0.2?? and >2??) in their ??¹⁸O and ??D. The slope of the local meteoric water line (??D?C??¹⁸O line), was 8.07?±?0.47, similar to that of global meteoric water line, confirming that the precipitation occurred under isotopic equilibrium, and was unaffected by some anomalous process; further, the evaporation of rain drops at the cloud base was insignificant. Whenever the isotopic variations were larger during a rain event (>2??) there was a significant negative correlation between the ??¹⁸O and DSD. The possible explanation is that larger drops are mostly associated with convective rather than stratiform rain, and ¹⁸O (and D) depletion in convective rain is relatively more. Bin-resolved microphysical models incorporating water isotopologues could benefit by considering drop size spectra, which could improve the match with stable isotope observations of precipitation.